A brief course in the teaching process

by George D. Strayer

6. It is well to remember that not merely number of observations counts in the solution of a problem. It is rather observations under varying conditions which give weight to our conclusions. One intensive observation may be worth a thousand careless ones.

7. When children are taken on excursions, great care must be exercised to keep them under proper guidance and control. The organization of children into smaller groups with leaders who are made responsible for their proper observance of directions will help. These leaders should have been over the ground with the teacher before the excursion. The assistance of parents, teachers, or of older pupils will at times be necessary.

8. There should be definite work periods during the excursion, just as in the schoolroom or laboratory.

9. A whistle, as a signal for assembling at one point, will help in out-of-door work, provided it is clearly understood that this signal must be obeyed immediately, and under all circumstances.

Comparison and abstraction: With the problem clearly defined and the data provided, the next step consists of comparison and the resulting abstraction of the element present in all of the cases which makes for the solution of the problem. In the ordinary course of our thinking the sequence is as follows: We find ourselves in a situation which presents a problem which demands an adjustment; we make a guess or formulate an hypothesis which furnishes the basis for our work in attempting to solve the problem; we gather data in the light of the hypothesis assumed, which, through comparison and abstraction, leads us to believe our hypothesis correct or false; if the hypothesis seems justified by the data gathered, it is further tested or verified by an appeal to experience; i.e. we endeavor to see whether our conclusion holds in all cases; if this test proves satisfactory, we generalize or define; and lastly this generalization or definition is used as a point of reference or truth to guide in later thinking or activity.

There is danger that we may overlook the very great importance of inference in this process. We cannot say just when this step in the process will be possible, but it is possibly the most significant of all. A situation presents a problem. Our success in solving the problem depends upon our ability to infer from the facts at our command. Often many inferences will be necessary before we succeed in finding the one that will stand the test. Again with the problem in mind we may be conscious of a great lack of data and may postpone our inference while we collect the needed information. There is one fallacy that must be carefully guarded against in dealing with children, as also with adults; namely, the tendency once the inference has been made to admit only such data as are found to support this particular hypothesis.

It is this ability to infer, to formulate a workable hypothesis, which distinguishes the genius from the man of mediocre ability. It is the ability to see facts in new relations, the giving of new meaning to facts which may be the common possession of all, that characterizes the great thinker. Other people knew many of the facts; but it took the mind of a Newton to discover the relationship existing among these data which he formulated in the law that all bodies attract each other directly in proportion to their weight and inversely in proportion to the square of the distance separating them. As we teach children we should encourage the intelligent guess. We would not, of course, encourage mere random guessing, which may be engaged in by children to have something to say or to blind the teacher. A child who offers a guess or hypothesis should be asked to give his ground for the inference, should show that his guess has grown out of his consideration of the data in hand. It is fallacious to suppose that this kind of thinking is beyond the power of children. They have been forming their inferences and testing them in action from the time that they began to act independently.

There is one element in the consideration of the step of comparison which cannot be too much emphasized, and that is that it is not the comparison of things or situations which present striking likenesses which gives rise to the highest type of thinking. To look at a dozen horses and then to conclude that all horses have four legs is merely a matter of classification; to observe that the sun, chemical action, electricity, and friction produce heat, and to arrive at the generalization from these cases, apparently so unlike, that heat is a mode of motion is the work of a genius. In general, it is safe to say that we would greatly strengthen our teaching if we were only more careful to see to it that our basis for generalization is found in situations presenting as many variations as possible. For example, if we want to teach a principle in arithmetic, the way to fix it and to make it available for further use by our pupils is not to get a number of problems all of which are alike in form and statement; but rather we should seek as great a variety as is possible in the language used or symbols employed that is compatible with the application of the principle to be taught. In an interesting article on reasoning in primary arithmetic, Professor Suzzallo has pointed out the fact that children’s difficulty in reasoning is often one of language.[8] The trouble has been that teachers have always used a set form, or a very few forms of expression, when they described situations which involved any one of the arithmetical processes. Later when the child is called upon to solve a problem involving this process he does not know which process to apply because he is unfamiliar with the form of expression used. To succeed in teaching children when to add involves the presentation of the situations which call for addition with as great a variation as is possible, i.e. by using not one form, but all of the words or phrases which may be used to indicate summation. In like manner in other fields the examples for comparison will be valuable in proportion as they present variety rather than uniformity in those elements which are not essential. Equally good illustration can be had from any other field. If we want pupils to get any adequate conception of the function of adjectives, we should use examples which involve a variety of adjectives in different parts of sentences. In geography the concept “river” will be clear only when the different types of rivers have been considered and the non-essential elements disregarded.

Generalization: When we feel that we have solved the problem, we are ready to state our generalization. There is considerable advantage in making such a statement. One can never be quite sure that he has solved his problem until he finds himself able to state clearly the results of his thinking. To attempt to define or to generalize is often to realize the inadequacy of our thought on the problem. Children should be encouraged to give their own definition or generalization before referring to that which is provided by the teacher or the book. Indeed, the significance of a generalization for further thinking or later action depends not simply upon one’s ability to repeat words, but rather upon adequate realization of the significance of the conclusion reached. The best test of such comprehension is found in the ability of the pupil to state the generalization for himself.